Displaying similar documents to “Generalized normal distributions.”

New metrics for weak convergence of distribution functions.

Michael D. Taylor (1985)

Stochastica

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Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which...

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

On independence in some families of multivariate distributions.

José Juan Quesada (1986)

Stochastica

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In this paper we will prove a characterization for the independence of random vectors with positive (negative) orthant dependence according to a direction. The result can be seen as a generalization of a result by Lehmann [4].

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

Metric similarities in the logic of approximation.

Michael Katz (1982)

Stochastica

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We describe restricted and extended versions of the logic of approximation which is meant to handle formally the problems of measurement error and of deduction under conditions of uncertainty. We apply the logic to the foundations of social and behavioral inquiry, axiomatizing in it an inexact similarity predicate which behaves like a metric approximation to identity. In the restricted version of the logic we formulate conditions for the imbeddability of similarity models in the real...